Simultaneous direct sum decompositions of several multivariate polynomials.
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| Title: | Simultaneous direct sum decompositions of several multivariate polynomials. |
|---|---|
| Authors: | Fang, Lishan1 (AUTHOR) fanglishan@hqu.edu.cn, Huang, Hua-Lin1 (AUTHOR) hualin.huang@hqu.edu.cn, Liao, Lili1 (AUTHOR) lili.liao@hqu.edu.cn |
| Source: | Linear Algebra & its Applications. Nov2025, Vol. 724, p320-335. 16p. |
| Subjects: | Homogeneous polynomials, Orthogonalization, Set theory, Idempotents, Polynomials |
| Abstract: | We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method. • Extend Harrison's center theory to a set of multivariate polynomials. • Discover the connection between simultaneous direct sum decompositions and centers. • Provide an algorithm for simultaneously decomposing multivariate polynomials. [ABSTRACT FROM AUTHOR] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 186643224 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Simultaneous direct sum decompositions of several multivariate polynomials. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fang%2C+Lishan%22">Fang, Lishan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fanglishan@hqu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Hua-Lin%22">Huang, Hua-Lin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hualin.huang@hqu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liao%2C+Lili%22">Liao, Lili</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lili.liao@hqu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Nov2025, Vol. 724, p320-335. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Homogeneous+polynomials%22">Homogeneous polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Orthogonalization%22">Orthogonalization</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Idempotents%22">Idempotents</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method. • Extend Harrison's center theory to a set of multivariate polynomials. • Discover the connection between simultaneous direct sum decompositions and centers. • Provide an algorithm for simultaneously decomposing multivariate polynomials. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2025.06.022 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 320 Subjects: – SubjectFull: Homogeneous polynomials Type: general – SubjectFull: Orthogonalization Type: general – SubjectFull: Set theory Type: general – SubjectFull: Idempotents Type: general – SubjectFull: Polynomials Type: general Titles: – TitleFull: Simultaneous direct sum decompositions of several multivariate polynomials. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fang, Lishan – PersonEntity: Name: NameFull: Huang, Hua-Lin – PersonEntity: Name: NameFull: Liao, Lili IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 724 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
| ResultId | 1 |
